A261996 The first of twenty-one consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.

8, 44, 128, 788, 2024, 5948, 15176, 87764, 223712, 655316, 1670312, 9654332, 24607376, 72079892, 183720224, 1061889836, 2706588728, 7928133884, 20207555408, 116798228708, 297700153784, 872022648428, 2222647375736, 12846743269124, 32744310328592

Offset: 1

Author

Colin Barker, Sep 08 2015

Keywords

• nonn
• easy

Comments

For the first of the corresponding four consecutive positive integers, see A261995.

Examples

			8 is in the sequence because 8^2 + ... + 28^2 = 7574 = 42^2 + ... + 45^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,110,-110,0,0,-1,1).

Crossrefs

Cf. A157092, A246642, A261995.

Programs

PARI

Vec(4*x*(x^8+3*x^7+3*x^6+9*x^5-89*x^4-165*x^3-21*x^2-9*x-2)/((x-1)*(x^8-110*x^4+1)) + O(x^40))

Formula

G.f.: 4*x*(x^8+3*x^7+3*x^6+9*x^5-89*x^4-165*x^3-21*x^2-9*x-2) / ((x-1)*(x^8-110*x^4+1)).